What Fit Hides: The Geometry of Few-Shot Subpopulation Repair

Two model updates can produce nearly identical changes in fixed edit-loss measurements yet generalize differently to the wider target subpopulation. We study this ambiguity in few-shot subpopulation repair, where a model is edited using a small correction set. A local geometric analysis quantifies how much held-out target improvement can remain ambiguous given identical or approximately matching edit measurements. With additional target, non-target, and reference probes, we construct a diagnostic update that achieves a specified local target improvement while minimizing a regularized non-target representation drift cost within the edit-gradient span. The same geometry predicts its locality advantage over the projected target-gradient update. Across six CIFAR-100 model runs, edit-loss differences shrink approximately quadratically with update size, while held-out target-score differences shrink approximately linearly. Using the same probes and matching validation improvement, the diagnostic achieves 16.1–18.5% higher model-median test target gain per unit off-target drift than the projected target gradient. Validation geometry predicts the projected-gradient-to-diagnostic test drift ratio without fitted calibration, with 4.31% median error relative to the excess ratio above one, compared with 22.04% for a leave-one-model-out constant predictor. The locality advantage remains with fewer probes and an additional edit-loss descent constraint. Paired continuations show that updates with the same immediate target improvement can have different effects after training resumes. Waterbirds and controlled ImageNet-20 reproduce the generalization and locality distinctions under a natural subgroup failure and with larger ResNet and ViT models.